# Topic 4 - Random Variables and Discrete Probability Distributions

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This article is a topic within the subject Business & Economic Statistics.

## Contents |

## Required Reading

Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition, pp. 217-243.

## Random Variables & Probability Distributions

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**X = Random Variable (RV)**-*A function or rule that assigns a number to an outcome of an experiment***Discrete RV**– A countable number of values - time, weight or height**Continuous RV**– Values are uncountable - the rugby, soccer or basketball score

**Probability Distribution**– Assigns a probability to the values of the RV P(X=x)

### Discrete Probability Distributions

### Laws of Expected Value

- E(c) = c
- E(X + c) = E(X) + c
- E(c*X) = c*E(X)
- E(X + Y) = E(X) + E(Y)

### Laws of Expected Variance

- V(c) = 0
- V (X + c) = V(X)
- V(c*X) = c^2 V(x)
- V(X + Y) = V(X) + V(Y) – 2COV(X,Y)

## Bivariate Distributions

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**Covariance**

This bi-variate distributions shows the join probabilities of X and Y. For example, the probability of X = 2 and Y = 1 is 0.03. The marginal probabilities can be found in the margins. E.g. the P(X=2) = 0.06 + 0.03 + 0.01 = 0.1

## End

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## References

**Textbook** refers to Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition,.